statsmodels.stats.stattools.robust_skewness¶

statsmodels.stats.stattools.robust_skewness(y, axis=0)[source]¶

Calculates the four skewness measures in Kim & White

Parameters:¶

yarray_like

Data to compute use in the estimator.

axisint or None, optional

Axis along which the skewness measures are computed. If None, the entire array is used.

Returns:¶

sk1ndarray

The standard skewness estimator.

sk2ndarray

Skewness estimator based on quartiles.

sk3ndarray

Skewness estimator based on mean-median difference, standardized by absolute deviation.

sk4ndarray

Skewness estimator based on mean-median difference, standardized by standard deviation.

Notes

The robust skewness measures are defined

$$S{K}_2=\frac{(q_{.75}-q_{.5})-(q_{.5}-q_{.25})}{q_{.75}-q_{.25}}$$

$$S{K}_3=\frac{\mu -{\hat{q}}_{0.5}}{\hat{E}\left[|y-\hat{\mu }|\right]}$$

$$S{K}_4=\frac{\mu -{\hat{q}}_{0.5}}{\hat{\sigma }}$$